Optimal. Leaf size=17 \[ \frac {1}{6} \sinh (3 x)+\frac {1}{10} \sinh (5 x) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {4283} \[ \frac {1}{6} \sinh (3 x)+\frac {1}{10} \sinh (5 x) \]
Antiderivative was successfully verified.
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Rule 4283
Rubi steps
\begin {align*} \int \cosh (x) \cosh (4 x) \, dx &=\frac {1}{6} \sinh (3 x)+\frac {1}{10} \sinh (5 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {1}{6} \sinh (3 x)+\frac {1}{10} \sinh (5 x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 34, normalized size = 2.00 \[ \frac {1}{10} \, \sinh \relax (x)^{5} + \frac {1}{6} \, {\left (6 \, \cosh \relax (x)^{2} + 1\right )} \sinh \relax (x)^{3} + \frac {1}{2} \, {\left (\cosh \relax (x)^{4} + \cosh \relax (x)^{2}\right )} \sinh \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.11, size = 27, normalized size = 1.59 \[ -\frac {1}{60} \, {\left (5 \, e^{\left (2 \, x\right )} + 3\right )} e^{\left (-5 \, x\right )} + \frac {1}{20} \, e^{\left (5 \, x\right )} + \frac {1}{12} \, e^{\left (3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.23, size = 14, normalized size = 0.82 \[ \frac {\sinh \left (3 x \right )}{6}+\frac {\sinh \left (5 x \right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.33, size = 27, normalized size = 1.59 \[ \frac {1}{60} \, {\left (5 \, e^{\left (-2 \, x\right )} + 3\right )} e^{\left (5 \, x\right )} - \frac {1}{12} \, e^{\left (-3 \, x\right )} - \frac {1}{20} \, e^{\left (-5 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.44, size = 15, normalized size = 0.88 \[ \frac {8\,{\mathrm {sinh}\relax (x)}^5}{5}+\frac {8\,{\mathrm {sinh}\relax (x)}^3}{3}+\mathrm {sinh}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 20, normalized size = 1.18 \[ - \frac {\sinh {\relax (x )} \cosh {\left (4 x \right )}}{15} + \frac {4 \sinh {\left (4 x \right )} \cosh {\relax (x )}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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